Output control of nonlinear systems using modified backstepping algorithm with disturbances compensation

Abstract

The article deals with an output tracking control system synthesis for a nonlinear plant functioning under bounded external disturbances which are not available for measurement. The plant is described by continuously differentiable functions with a determinable dynamic relative degree. The disturbance function fulfills the Lipschitz condition. The standard model transformations are used to get a model of error dynamics. The algorithm synthesis process is based on iterative procedure with a number of steps equal to the order of the plant relative dynamic degree. A proposed solution is a robust modification of the backstepping approach with the similar controller design structure. The main changes are based on plant model transformations that make it possible to use the only one filer in control system and, along with it, an auxiliary loop method is used for disturbances evaluation and compensation. The auxiliary loop method leads to introduce a model of desired dynamics of errors on each step of the backstepping procedure and estimates the value of disturbance influences. High-gain observers are used for unknown signals measuring together with their derivatives. Tracking errors and observation errors convergence with the adjustable accuracy during the finite transient time is proved. The efficiency of the algorithm is demonstrated using computer modeling. The performance comparison between the proposed method and the immediate analogue are shown and some quality indicators are obtained. The algorithm is additionally tested using the model of laboratory helicopter-like platform «Twin Rotor MIMO System» to demonstrate the practical importance of the research.